CN110704805B - Pre-stressed concrete beam bridge cracking early warning method based on live load strain - Google Patents
Pre-stressed concrete beam bridge cracking early warning method based on live load strain Download PDFInfo
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Abstract
The invention discloses a pre-stressed concrete beam bridge cracking early warning method based on live load strain, which comprises the following steps: collecting strain influence line amplitude data of a bridge member when a vehicle passes each time, and drawing a frequency histogram of the strain influence line amplitude data; fitting vertex coordinates of each rectangular histogram of the strain influence line amplitude data frequency histogram by using a least square method by taking a Gaussian mixture model as a target function, and normalizing integral values of the fitting function in a negative infinite interval to a positive infinite interval; determining a boundary value of each peak interval in the Gaussian mixture model function, and performing data clustering on the amplitude data of the strain influence line according to the boundary value of each interval; and taking the data cluster with the maximum mean value as a strain influence line amplitude data cluster under the action of heavy vehicles, taking a strain value corresponding to the cumulative distribution function of the data cluster at a specific guarantee rate as an early warning index for reflecting concrete cracking, and carrying out early warning. Compared with the prior art, the method is accurate and reasonable, has definite physical significance and comprehensive consideration factors.
Description
Technical Field
The invention belongs to the field of monitoring, detecting, early warning and evaluating of existing bridge structure performance, and relates to a pre-stressed concrete beam bridge cracking early warning method based on live-load strain, in particular to a pre-stressed concrete beam bridge cracking early warning method based on long-term test data of bridge vehicle-mounted strain influence line amplitude.
Background
The prestressed concrete beam bridge is a common design and construction type of medium and small span bridges on Chinese traffic network lines, and the main performance of the prestressed concrete beam bridge is the concrete cracking disease in the service process. With the development of testing technology, on-line monitoring and early warning of bridge structure cracking diseases driven by data become possible. The vehicle-mounted strain influence line has a clear signal starting point, so that the structure load effect can be accurately calibrated and quantized, and the long-term performance evolution process of the structure is reflected.
At present, the method for early warning the crack of the prestressed concrete beam bridge based on test data in the civil engineering and traffic fields is less, and the related method for carrying out long-term and real-time early warning on the bridge based on the sensor time sequence data is less. The following methods are commonly used: (1) crack diseases are found based on the manual inspection result: according to the method, a bridge manager approaches a position where a bridge is easy to crack, observes and discovers concrete apparent diseases, and reports the concrete apparent diseases to a technician for later maintenance and reinforcement, the method depends on the labor and subjective judgment of the bridge management personnel, and the personnel approaches the position where the bridge is easy to crack, so that time and labor are wasted, danger exists, and the method is uneconomical; (2) directly judging whether cracking occurs based on the test strain data: the method uses the strain value measured by a sensor in the bridge monitoring and detecting process to convert a stress value (known concrete elastic modulus), when the stress value is greater than the limit/design tensile strength given by the specification, the concrete structure is judged to crack, the method is too ideal, the consideration factor is too few (for example, the strain caused by temperature can not equivalently generate stress), the prestressed structure is allowed to work with cracks, and the microcracks under the heavy load action are closed due to the prestress effect after the load disappears, so the method is lack of rationality; (3) identifying cracking diseases through image data: the method generally adopts a neural network to deeply learn the characteristics of the crack image and identifies whether cracks exist in the image obtained by a high-definition camera and an unmanned aerial vehicle.
Therefore, it is necessary to develop a method with clear physical significance, low technical threshold, aiming at the time sequence data of the commonly used sensors and easy application and implementation, so as to realize the crack early warning of the existing prestressed concrete beam bridge.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method can realize the early warning of the cracking diseases of the existing prestressed concrete beam bridge in the service period based on live load strain data.
In order to solve the technical problems, the invention adopts the technical scheme that:
a pre-stressed concrete beam bridge cracking early warning method based on live load strain comprises the following steps:
(1) Collecting the time courses of the strain influence lines of all the members of the bridge when a vehicle passes through each time, extracting the amplitude data of each time course of the strain influence lines, accumulating a certain amount of amplitude data of the strain influence lines, and drawing a frequency histogram of the long-term data of the amplitude of the strain influence lines;
(2) Fitting vertex coordinates of each rectangular histogram of the strain influence line amplitude data frequency histogram by using a least square method by taking a Gaussian mixture model as a target function, normalizing an integral value of the fitting function in a range from minus infinity to plus infinity into 1, and checking the fitting goodness;
(3) Determining a boundary value (trough or inflection point) of each single peak interval in the mixed Gaussian model function according to each peak value of the corresponding mixed Gaussian model, and performing data clustering on the amplitude data of the strain influence line according to the boundary value of each single peak interval to form a plurality of data clusters;
(4) And taking a data cluster corresponding to a single peak interval with the maximum mean value in the Gaussian mixture model as a strain influence line amplitude data cluster under the action of a heavy vehicle, taking a strain value corresponding to an accumulative distribution function of the data cluster at a specific guarantee rate as an early warning index for reflecting concrete cracking, and further comparing the index with a limit value of a limit tensile strain specification of a concrete material to realize early warning.
Preferably, the step (1) is specifically as follows:
(1.1) acquiring the time course of the strain influence line of each member of the bridge when a vehicle passes through each time, and independently extracting and storing the amplitude data of each time course of the strain influence line at each strain measuring point;
and (1.2) drawing respective frequency histograms based on the strain influence line amplitude long-term data of each strain measuring point sensor.
In a preferred embodiment, the step (2) includes:
(2.1) taking a Gaussian mixture model as an objective function:
adopting a least square method:
min(∑||f(x j )-y j ||)
fitting vertex coordinates of each rectangular vertical direction of a strain influence line data frequency histogram, wherein Y-axis coordinates of the vertex are frequencies of each rectangular vertical direction, and X-axis coordinates of the vertex are median values of strain intervals of each rectangular vertical direction;
(2.2) integrating the fitted Gaussian mixture model function in a negative infinite-to-positive infinite interval, normalizing the function integral value to 1, and directly shifting the normalization coefficient of the integral function into an integral sign according to the integral principle to be used as the normalization coefficient of the Gaussian mixture model function;
and (2.3) taking the normalized mixed Gaussian model function as a probability density function of the amplitude value of the strain influence line, taking an integral function of the mixed Gaussian model function as a probability distribution function of the amplitude value of the strain influence line, and testing the goodness of fit of the probability distribution function by adopting a general method such as Kolmogorov-Smirnov test and the like.
Preferably, the step (3) comprises the following steps:
(3.1) determining a boundary value of each single peak interval in the Gaussian mixture model function according to each peak value of the corresponding Gaussian mixture model, wherein the boundary value is usually a valley point (minimum point) between each peak, and if no valley point exists, an inflection point between the mean values of the Gaussian functions corresponding to two single peak intervals is taken;
and (3.2) carrying out data clustering on the amplitude data of the strain influence lines according to the boundary value of each single peak interval to form a plurality of data clusters based on a Gaussian mixture model.
Preferably, step (4) includes:
(4.1) taking a data cluster corresponding to a single peak interval with the maximum mean value in the Gaussian mixture model as a strain influence line amplitude data cluster under the action of the heavy vehicle;
(4.2) integrating the Gaussian functions (usually only containing 1 Gaussian function) corresponding to the data clusters in the interval from minus infinity to plus infinity, and normalizing the function integral value to 1:
taking the normalized Gaussian function as a probability density function of the amplitude value of the heavy vehicle strain influence line, and taking an integral function of the Gaussian function as a probability distribution function of the amplitude value of the heavy vehicle strain influence line;
(4.3) taking a strain value (alpha) corresponding to the probability distribution function (namely the cumulative distribution function) of the amplitude of the stress influence line of the heavy vehicle at a specific guarantee rate (beta, if the beta is 95%) as an early warning index for reflecting the concrete cracking:
wherein P (x ≦ α) is the probability of α or more in the amplitude data of the stress-influence line for heavy-duty vehicles, which is equal to the cumulative distribution function (F) K (x ≦ α)); and comparing the index alpha with the limit value of the limit tensile strain specification of the concrete material (obtained by dividing the limit tensile strength or the design tensile strength in the specification by the elastic modulus of the concrete material), wherein the value of alpha slowly approaches and then exceeds the limit value of the specification along with the gradual degradation of the bridge, and when the value of alpha is greater than the standard value, an alarm is given.
Compared with the prior art, the invention has the following beneficial effects:
(1) The method for early warning the cracking of the prestressed concrete beam bridge is based on vehicle-mounted strain influence line amplitude data, the vehicle-mounted strain amplitude is directly related to the tensile stress of concrete, and the structural cracking is mainly generated by the tensile stress of the concrete, so that the method for calculating the early warning index by using the statistical value of the vehicle-mounted strain amplitude data is quite reasonable, has definite physical significance and is convenient for bridge management and maintenance personnel to understand and implement.
(2) The implementation process of the invention is basically established on the basis of statistical analysis and calculation of test data, the experience factors are few, and any technician with certain mathematical and statistical bases can realize the pre-warning method for the cracking of the prestressed concrete beam bridge based on live load strain according to the patent. The method has strong feasibility and is convenient for wide popularization and application.
3) The method is rigorous in logic and comprehensive in consideration factors, the pre-stressed concrete beam bridge cracking early warning is realized by using statistical parameters of vehicle-mounted strain amplitude data, a vehicle-mounted strain influence line has a definite signal starting point (zero point), the amplitude of the vehicle-mounted strain influence line can be accurately calibrated and quantify a load effect, meanwhile, the influence of temperature change on a strain test value is eliminated, and the method is based on rigorous logical deduction and eliminates possible interference factors.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a fitting of the strain influence line amplitude frequency histogram to its Gaussian mixture model.
FIG. 3 is a schematic diagram of amplitude data clustering of vehicle-mounted strain influence lines.
FIG. 4 is a schematic diagram of crack early warning based on load-break strain influence line amplitude data cluster probability characteristics.
Detailed Description
The technical solution of the present invention will be described in detail with reference to the accompanying drawings.
As shown in FIG. 1, the embodiment of the invention discloses a pre-warning method for cracking of a prestressed concrete beam bridge based on live load strain, which mainly comprises the following steps:
step 10): acquiring the time courses of the strain influence lines of all the members of the bridge when a vehicle passes through each time, and independently extracting and storing the amplitude data of each time course of the strain influence lines at each strain measuring point; and drawing respective frequency histograms based on the strain influence line amplitude long-term data of each strain measuring point sensor.
Step 20): taking a Gaussian mixture model as an objective function:
adopting a least square method:
min(∑||f(x j )-y j ||)
fitting vertex coordinates of each rectangular vertical direction of a strain influence line data frequency histogram, wherein Y-axis coordinates of the vertex are frequencies of each rectangular vertical direction, and X-axis coordinates of the vertex are median values of strain intervals of each rectangular vertical direction; integrating the fitted Gaussian mixture model function in a negative infinite-to-positive infinite interval, normalizing the function integral value to 1, and according to the integral principle, directly shifting the normalization coefficient of the integral function into an integral sign to be used as the normalization coefficient of the Gaussian mixture model function; and (3) taking the normalized mixed Gaussian model function as a probability density function of the amplitude of the strain influence line, taking the integral function of the mixed Gaussian model function as a probability distribution function of the amplitude of the strain influence line, and testing the goodness of fit of the probability distribution function by adopting a Kolmogorov-Smirnov test and other general methods.
Step 30): determining a boundary value of each single peak interval in the mixed Gaussian model function according to each peak value of the corresponding mixed Gaussian model, wherein the boundary value usually takes a valley point (minimum point) between each peak, and takes an inflection point between the mean values of the Gaussian functions corresponding to two single peak intervals when no valley point exists; and carrying out data clustering on the amplitude data of the strain influence lines according to the boundary value of each single peak interval to form a plurality of data clusters based on a Gaussian mixture model.
Step 40): taking a data cluster corresponding to a single peak interval with the maximum mean value in the Gaussian mixture model as a strain influence line amplitude data cluster under the action of a heavy vehicle; integrating the Gaussian function (usually only containing 1 Gaussian function) corresponding to the data cluster in the interval from minus infinity to plus infinity, and normalizing the function integral value to 1:
taking the normalized Gaussian function as a probability density function of the amplitude value of the heavy vehicle strain influence line, and taking an integral function of the Gaussian function as a probability distribution function of the amplitude value of the heavy vehicle strain influence line; taking a strain value (alpha) corresponding to a probability distribution function (namely an accumulative distribution function) of the amplitude of the stress influence line of the heavy vehicle at a specific guarantee rate (beta, if the beta is 95%) as an early warning index for reflecting the concrete cracking:
wherein P (x ≦ α) is the probability of α or more in the data of the amplitude of the strain-influencing line of the heavy vehicle, which is equal to the cumulative distribution function (F) K (x ≦ α)); and comparing the index alpha with the limit value of the limit tensile strain specification of the concrete material (obtained by dividing the limit tensile strength or the design tensile strength in the specification by the elastic modulus of the concrete material), wherein the value of alpha slowly approaches and then exceeds the limit value of the specification along with the gradual degradation of the bridge, and when the value of alpha is greater than the standard value, an alarm is given.
Example 1:
the specific implementation process of the invention is described below by taking the long-term data of the vehicle-mounted strain influence line amplitude obtained by a longitudinal strain sensor of a 25-meter prestressed concrete combined box girder bridge on a certain box girder bottom plate of a certain span of a large bridge of a roach of Jiangsu province as an example.
(1) The method comprises the steps of collecting longitudinal strain influence line time courses of a bottom plate of a certain box girder of a bridge when a vehicle passes through each time, extracting and storing amplitude data of each strain influence line time course, drawing respective frequency histograms (shown in figure 2) based on the strain influence line amplitude long-term data, wherein the frequency histograms in the example take 200 rectangular histograms in the range of about 0-70 mu epsilon.
(2) Fitting vertex coordinates of each rectangular vertical direction of a strain influence line amplitude data frequency histogram by using a least square method by using a mixed Gaussian model as a target function, wherein the fitted Gaussian distribution model has 3 obvious peaks, the first peak comprises 2 Gaussian functions, and the second peak and the third peak respectively comprise 1 Gaussian function (as shown in figure 2); integrating the fitted mixed Gaussian model function in a negative infinite interval to a positive infinite interval, and normalizing the integral value of the function to 1; and (3) taking the normalized mixed Gaussian model function as a probability density function of the amplitude of the strain influence line, taking the integral function of the mixed Gaussian model function as a probability distribution function of the amplitude of the strain influence line, and testing the goodness of fit of the fitting probability distribution function under the 0.05 significance level by adopting a Kolmogorov-Smirnov test method.
(3) Determining a boundary value (such as a trough value circled in fig. 2) of each single peak interval in the Gaussian mixture model function according to each peak value of the corresponding Gaussian mixture model; and (3) carrying out data clustering on the amplitude data of the strain influence lines according to the boundary value of each single peak interval to form 3 data clusters based on a Gaussian mixture model (as shown in figure 3).
(4) Taking a data cluster 3 corresponding to a third peak in the Gaussian mixture model as a strain influence line amplitude data cluster under the action of the heavy vehicle; integrating a Gaussian function corresponding to the data cluster 3 in a negative infinite interval to a positive infinite interval, normalizing a function integral value to be 1, taking the normalized Gaussian function as a probability density function of the amplitude value of the stress influence line of the heavy vehicle, and taking an integral function of the normalized Gaussian function as a probability distribution function of the amplitude value of the stress influence line of the heavy vehicle; taking a strain value (alpha) corresponding to a 95% guarantee rate of a probability distribution function (namely an accumulated distribution function) of the amplitude of the heavy vehicle strain influence line as an early warning index for reflecting concrete cracking, and comparing the value (alpha =38.93 mu epsilon in the example) of the early warning index alpha with the limit cracking strain 76.52 mu epsilon (obtained by converting the limit tensile strength in the specification) and the design cracking strain 54.78 mu epsilon (obtained by converting the design tensile strength in the specification) of the C50 concrete material (as shown in FIG. 4); when alpha is larger than the designed cracking strain, a weak alarm is sent out, and when alpha is larger than the limit cracking strain, a strong alarm is sent out.
The above embodiments are merely further illustrative of the present invention, and various modifications and substitutions of equivalent forms to those skilled in the art after reading the embodiments of the present invention are within the scope of the present invention as defined in the appended claims.
Claims (5)
1. A prestressed concrete beam bridge cracking early warning method based on live load strain is characterized by comprising the following steps:
(1) Collecting the time courses of strain influence lines of all members of a bridge when a vehicle passes through each time, extracting the amplitude data of each time course of strain influence lines, accumulating a certain amount of data of the amplitude data of the strain influence lines, and drawing a frequency or frequency histogram of long-term data of the amplitude of the strain influence lines;
(2) Fitting vertex coordinates of each rectangular histogram of the strain influence line amplitude data frequency or frequency histogram by using a least square method by taking a Gaussian mixture model as a target function, normalizing an integral value of the fitting function in a range from minus infinity to plus infinity to be 1, and checking the fitting goodness of the integral value;
(3) Determining a boundary value of each single peak interval in the mixed Gaussian model function according to each peak value of the corresponding mixed Gaussian model, and performing data clustering on the amplitude data of the strain influence line according to the boundary value of each single peak interval to form a plurality of data clusters;
(4) Taking a data cluster corresponding to a single peak interval with the maximum mean value in the Gaussian mixture model as a strain influence line amplitude data cluster under the action of a heavy vehicle, taking a strain value alpha corresponding to an accumulative distribution function of the data cluster at a specific guarantee rate beta as an early warning index for reflecting concrete cracking,
wherein P (x is less than or equal to alpha) is the probability of more than or equal to alpha in the amplitude data of the stress influence line of the heavy vehicle, and is equal to the cumulative distribution function F K (x is less than or equal to alpha); and comparing the index with the limit value of the limit tensile strain specification of the concrete material and realizing early warning.
2. The live load strain-based prestressed concrete beam bridge cracking early warning method according to claim 1, wherein the step (1) specifically comprises:
(1.1) acquiring a strain influence line time course of each member of the bridge when a vehicle passes through each time, and independently extracting and storing amplitude data of each strain influence line time course at each strain measuring point;
and (1.2) drawing respective frequency or frequency histograms based on the strain influence line amplitude long-term data of each strain measuring point sensor.
3. The live load strain-based prestressed concrete beam bridge cracking early-warning method according to claim 1, wherein the step (2) comprises:
(2.1) fitting vertex coordinates of each rectangular histogram of the strain influence line amplitude data frequency or frequency histogram by using a least square method by taking a Gaussian mixture model as a target function, wherein Y-axis coordinates of a vertex are the frequency or frequency of each rectangular histogram, and X-axis coordinates of the vertex are strain interval median values of each rectangular histogram;
the general expression of the Gaussian mixture model is as follows:
the general formula for the least squares method is:
min(∑||f(x j )-y j ||)
(2.2) integrating the fitted Gaussian mixture model function in a negative infinite-to-positive infinite interval, normalizing the function integral value to 1, and directly shifting the normalization coefficient of the integral function into an integral sign to be used as the normalization coefficient of the Gaussian mixture model function;
and (2.3) taking the normalized mixed Gaussian model function as a probability density function of the amplitude of the strain influence line, taking an integral function of the mixed Gaussian model function as a probability distribution function of the amplitude of the strain influence line, and testing the goodness of fit of the probability distribution function by adopting a Chi-square test method and a Kolmogorov-Smirnov test method.
4. The live load strain-based prestressed concrete beam bridge cracking early warning method according to claim 1, wherein the step (3) specifically comprises:
(3.1) determining a boundary value of each single peak interval in the Gaussian mixture model function according to each peak value of the corresponding Gaussian mixture model, wherein the boundary value is a valley point between every two peaks, and if no valley point exists, an inflection point between Gaussian function mean values corresponding to two single peak intervals is taken;
and (3.2) carrying out data clustering on the amplitude data of the strain influence lines according to boundary values of single peak intervals to form a plurality of data clusters based on a Gaussian mixture model.
5. The live load strain-based prestressed concrete beam bridge cracking early warning method according to claim 1, wherein the step (4) specifically comprises:
(4.1) taking a data cluster corresponding to a single peak interval with the maximum mean value in the Gaussian mixture model as a strain influence line amplitude data cluster under the action of a heavy vehicle;
(4.2) integrating the Gaussian function corresponding to the data cluster in a negative infinite interval to a positive infinite interval, and normalizing the function integral value to 1:
taking the normalized Gaussian function as a probability density function of the amplitude value of the stress influence line of the heavy vehicle, and taking an integral function of the Gaussian function as a probability distribution function of the amplitude value of the stress influence line of the heavy vehicle;
(4.3) taking a strain value alpha corresponding to the specific guarantee rate beta of the probability distribution function of the amplitude of the stress influence line of the heavy truck as an early warning index for reflecting the concrete cracking:
wherein P (x is less than or equal to alpha) is the probability of more than or equal to alpha in the amplitude data of the stress influence line of the heavy vehicle, and is equal to the cumulative distribution function F K (x is less than or equal to alpha); and comparing the index alpha with the limit value of the limit tensile strain specification of the concrete material, and when the alpha is greater than the specification value, indicating that the live load strain of the test is frequently exceeded, and then giving an alarm to a management and maintenance unit.
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